Problem: Simplify the following expression: $ t = 3 - \dfrac{z + 7}{-9} $
Answer: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-9}{-9}$ $ \dfrac{3}{1} \times \dfrac{-9}{-9} = \dfrac{-27}{-9} $ Therefore $ t = \dfrac{-27}{-9} - \dfrac{z + 7}{-9} $ Now the expressions have the same denominator we can simply subtract the numerators: $t = \dfrac{-27 - (z + 7) }{-9} $ Distribute the negative sign: $t = \dfrac{-27 - z - 7}{-9}$ $t = \dfrac{-z - 34}{-9}$ Simplify the expression by dividing the numerator and denominator by -1: $t = \dfrac{z + 34}{9}$